{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import pandas as pd \n",
    "import scipy.stats as stats \n",
    "import scipy\n",
    "# import pymysql  \n",
    "\n",
    "from datetime import datetime \n",
    "import statsmodels.formula.api as smf  \n",
    "\n",
    "\n",
    "from matplotlib import style\n",
    "import matplotlib.pyplot as plt \n",
    "import matplotlib.dates as mdates\n",
    "\n",
    "from matplotlib.font_manager import FontProperties \n",
    "from pylab import mpl\n",
    "#mpl.rcParams['font.sans-serif'] = ['SimHei']\n",
    "#plt.rcParams['font.family'] = 'Times New Roman'\n",
    "\n",
    "\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "from IPython.core.interactiveshell import InteractiveShell \n",
    "\n",
    "InteractiveShell.ast_node_interactivity = 'all'\n",
    "\n",
    "\n",
    "pd.set_option('display.max_columns', None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.microsoft.datawrangler.viewer.v0+json": {
       "columns": [
        {
         "name": "Day",
         "rawType": "datetime64[ns]",
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         "name": "Preclose",
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         "type": "string"
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         "name": "Open",
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         "type": "float"
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         "name": "Highest",
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         "name": "Close",
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         "type": "float"
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         "1990-12-28 00:00:00",
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         "1990-12-31 00:00:00",
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         "1991-01-02 00:00:00",
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         "1991-01-07 00:00:00",
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         "1991-01-08 00:00:00",
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         "1991-01-09 00:00:00",
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         "1991-01-10 00:00:00",
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         "1991-01-11 00:00:00",
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         "134.6"
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         "1991-01-14 00:00:00",
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         "135.19",
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         "1991-01-15 00:00:00",
         "134.67",
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         "1991-01-16 00:00:00",
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         "134.14",
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         "1991-01-17 00:00:00",
         "134.24",
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        [
         "1991-01-18 00:00:00",
         "134.25",
         "133.7",
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         "1991-01-21 00:00:00",
         "134.24",
         "133.7",
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        [
         "1991-01-22 00:00:00",
         "134.24",
         "133.72",
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         "1991-01-23 00:00:00",
         "133.72",
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         "1991-01-24 00:00:00",
         "133.17",
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         "1991-01-30 00:00:00",
         "130.95",
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         "1991-01-31 00:00:00",
         "130.44",
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         "1991-02-01 00:00:00",
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         "1991-02-05 00:00:00",
         "129.05",
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         "1991-02-11 00:00:00",
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         "1991-02-12 00:00:00",
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         "1991-02-13 00:00:00",
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         "1991-02-19 00:00:00",
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         "1991-02-21 00:00:00",
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         "1991-02-25 00:00:00",
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         "1991-02-26 00:00:00",
         "134.4",
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         "133.9",
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         "1991-02-27 00:00:00",
         "133.93",
         "133.44",
         "133.98",
         "133.44",
         "133.47"
        ],
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         "1991-02-28 00:00:00",
         "133.47",
         "132.99",
         "133.52",
         "132.98",
         "133.01"
        ],
        [
         "1991-03-01 00:00:00",
         "133.01",
         "132.53",
         "132.53",
         "132.47",
         "132.53"
        ]
       ],
       "shape": {
        "columns": 5,
        "rows": 8473
       }
      },
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Preclose</th>\n",
       "      <th>Open</th>\n",
       "      <th>Highest</th>\n",
       "      <th>Lowest</th>\n",
       "      <th>Close</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-12-19</th>\n",
       "      <td></td>\n",
       "      <td>96.050</td>\n",
       "      <td>99.980</td>\n",
       "      <td>95.790</td>\n",
       "      <td>99.980</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-20</th>\n",
       "      <td>99.98</td>\n",
       "      <td>104.300</td>\n",
       "      <td>104.390</td>\n",
       "      <td>99.980</td>\n",
       "      <td>104.390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-21</th>\n",
       "      <td>104.39</td>\n",
       "      <td>109.070</td>\n",
       "      <td>109.130</td>\n",
       "      <td>103.730</td>\n",
       "      <td>109.130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-24</th>\n",
       "      <td>109.13</td>\n",
       "      <td>113.570</td>\n",
       "      <td>114.550</td>\n",
       "      <td>109.130</td>\n",
       "      <td>114.550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-25</th>\n",
       "      <td>114.55</td>\n",
       "      <td>120.090</td>\n",
       "      <td>120.250</td>\n",
       "      <td>114.550</td>\n",
       "      <td>120.250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-08-25</th>\n",
       "      <td>3825.759</td>\n",
       "      <td>3848.163</td>\n",
       "      <td>3883.562</td>\n",
       "      <td>3839.972</td>\n",
       "      <td>3883.562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-08-26</th>\n",
       "      <td>3883.562</td>\n",
       "      <td>3871.471</td>\n",
       "      <td>3888.599</td>\n",
       "      <td>3859.758</td>\n",
       "      <td>3868.382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-08-27</th>\n",
       "      <td>3868.382</td>\n",
       "      <td>3869.612</td>\n",
       "      <td>3887.198</td>\n",
       "      <td>3800.350</td>\n",
       "      <td>3800.350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-08-28</th>\n",
       "      <td>3800.35</td>\n",
       "      <td>3796.711</td>\n",
       "      <td>3845.087</td>\n",
       "      <td>3761.422</td>\n",
       "      <td>3843.597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-08-29</th>\n",
       "      <td>3843.597</td>\n",
       "      <td>3842.823</td>\n",
       "      <td>3867.606</td>\n",
       "      <td>3839.206</td>\n",
       "      <td>3857.927</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8473 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Preclose      Open   Highest    Lowest     Close\n",
       "Day                                                         \n",
       "1990-12-19              96.050    99.980    95.790    99.980\n",
       "1990-12-20     99.98   104.300   104.390    99.980   104.390\n",
       "1990-12-21    104.39   109.070   109.130   103.730   109.130\n",
       "1990-12-24    109.13   113.570   114.550   109.130   114.550\n",
       "1990-12-25    114.55   120.090   120.250   114.550   120.250\n",
       "...              ...       ...       ...       ...       ...\n",
       "2025-08-25  3825.759  3848.163  3883.562  3839.972  3883.562\n",
       "2025-08-26  3883.562  3871.471  3888.599  3859.758  3868.382\n",
       "2025-08-27  3868.382  3869.612  3887.198  3800.350  3800.350\n",
       "2025-08-28   3800.35  3796.711  3845.087  3761.422  3843.597\n",
       "2025-08-29  3843.597  3842.823  3867.606  3839.206  3857.927\n",
       "\n",
       "[8473 rows x 5 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('datasets/000001.csv')\n",
    "data['Day'] = pd.to_datetime(data['Day'],format='%Y/%m/%d')\n",
    "data.set_index('Day', inplace = True)\n",
    "data.sort_values(by = ['Day'],axis=0, ascending=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.microsoft.datawrangler.viewer.v0+json": {
       "columns": [
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         "name": "Day",
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        },
        {
         "name": "Open",
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        },
        {
         "name": "Highest",
         "rawType": "float64",
         "type": "float"
        },
        {
         "name": "Lowest",
         "rawType": "float64",
         "type": "float"
        },
        {
         "name": "Close",
         "rawType": "float64",
         "type": "float"
        },
        {
         "name": "Raw_return",
         "rawType": "float64",
         "type": "float"
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         "1995-02-06 00:00:00",
         "562.59",
         "559.78",
         "559.84",
         "532.91",
         "533.72",
         "-0.05131623384702888"
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        [
         "1995-02-07 00:00:00",
         "533.72",
         "532.11",
         "536.63",
         "524.43",
         "532.49",
         "-0.0023045791800944126"
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        [
         "1995-02-08 00:00:00",
         "532.49",
         "533.09",
         "537.55",
         "531.22",
         "533.75",
         "0.0023662416195608937"
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        [
         "1995-02-09 00:00:00",
         "533.75",
         "533.79",
         "553.36",
         "533.14",
         "553.36",
         "0.03674004683840759"
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        [
         "1995-02-10 00:00:00",
         "553.36",
         "548.77",
         "558.95",
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         "1995-02-13 00:00:00",
         "541.38",
         "537.95",
         "550.25",
         "537.05",
         "548.84",
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         "1995-02-14 00:00:00",
         "548.84",
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         "552.35",
         "542.18",
         "548.11",
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         "1995-02-15 00:00:00",
         "548.11",
         "547.83",
         "548.69",
         "542.5",
         "542.84",
         "-0.00961485833135678"
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        [
         "1995-02-16 00:00:00",
         "542.84",
         "542.26",
         "542.82",
         "537.21",
         "538.37",
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         "1995-02-17 00:00:00",
         "538.37",
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         "1995-02-20 00:00:00",
         "533.76",
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         "540.86",
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         "1995-02-21 00:00:00",
         "534.96",
         "536.07",
         "541.14",
         "535.97",
         "541.14",
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        [
         "1995-02-22 00:00:00",
         "541.14",
         "541.21",
         "594.81",
         "541.21",
         "594.64",
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        [
         "1995-02-23 00:00:00",
         "594.64",
         "589.9",
         "611.89",
         "575.82",
         "589.13",
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         "1995-02-24 00:00:00",
         "589.13",
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         "594.92",
         "555.2",
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         "1995-02-27 00:00:00",
         "558.43",
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         "559.04",
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         "1995-02-28 00:00:00",
         "561.27",
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         "544.06",
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         "1995-03-01 00:00:00",
         "549.26",
         "548.91",
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         "545.72",
         "556.96",
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         "1995-03-02 00:00:00",
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         "1995-03-03 00:00:00",
         "560.85",
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        [
         "1995-03-06 00:00:00",
         "577.22",
         "585.24",
         "616.76",
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        [
         "1995-03-07 00:00:00",
         "616.3",
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        [
         "1995-03-08 00:00:00",
         "632.96",
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         "634.2",
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         "1995-03-09 00:00:00",
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         "1995-03-10 00:00:00",
         "605.59",
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         "600.51",
         "583.72",
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        [
         "1995-03-13 00:00:00",
         "586.29",
         "596.65",
         "597.18",
         "583.38",
         "586.23",
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        [
         "1995-03-14 00:00:00",
         "586.23",
         "588.18",
         "599.9",
         "586.19",
         "588.24",
         "0.003428688398751323"
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        [
         "1995-03-15 00:00:00",
         "588.24",
         "588.78",
         "591.49",
         "568.6",
         "572.6",
         "-0.026587787297701615"
        ],
        [
         "1995-03-16 00:00:00",
         "572.6",
         "570.51",
         "579.88",
         "569.17",
         "579.88",
         "0.012713936430317707"
        ],
        [
         "1995-03-17 00:00:00",
         "579.88",
         "579.62",
         "593.97",
         "577.91",
         "593.52",
         "0.02352210802234933"
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        [
         "1995-03-20 00:00:00",
         "593.52",
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         "604.96",
         "585.15",
         "585.45",
         "-0.01359684593610988"
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       ],
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      },
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       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Preclose</th>\n",
       "      <th>Open</th>\n",
       "      <th>Highest</th>\n",
       "      <th>Lowest</th>\n",
       "      <th>Close</th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-03</th>\n",
       "      <td>647.870</td>\n",
       "      <td>637.720</td>\n",
       "      <td>647.710</td>\n",
       "      <td>630.530</td>\n",
       "      <td>639.880</td>\n",
       "      <td>-0.012333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-04</th>\n",
       "      <td>639.880</td>\n",
       "      <td>641.900</td>\n",
       "      <td>655.510</td>\n",
       "      <td>638.860</td>\n",
       "      <td>653.810</td>\n",
       "      <td>0.021770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-05</th>\n",
       "      <td>653.810</td>\n",
       "      <td>655.380</td>\n",
       "      <td>657.520</td>\n",
       "      <td>645.810</td>\n",
       "      <td>646.890</td>\n",
       "      <td>-0.010584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-06</th>\n",
       "      <td>646.890</td>\n",
       "      <td>642.750</td>\n",
       "      <td>643.890</td>\n",
       "      <td>636.330</td>\n",
       "      <td>640.760</td>\n",
       "      <td>-0.009476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-09</th>\n",
       "      <td>640.760</td>\n",
       "      <td>637.520</td>\n",
       "      <td>637.550</td>\n",
       "      <td>625.040</td>\n",
       "      <td>626.000</td>\n",
       "      <td>-0.023035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-24</th>\n",
       "      <td>2748.918</td>\n",
       "      <td>2770.754</td>\n",
       "      <td>2863.152</td>\n",
       "      <td>2761.372</td>\n",
       "      <td>2863.126</td>\n",
       "      <td>0.041547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-25</th>\n",
       "      <td>2863.126</td>\n",
       "      <td>2901.419</td>\n",
       "      <td>2952.451</td>\n",
       "      <td>2889.048</td>\n",
       "      <td>2896.306</td>\n",
       "      <td>0.011589</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-26</th>\n",
       "      <td>2896.306</td>\n",
       "      <td>2893.745</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>2889.014</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>0.036131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-27</th>\n",
       "      <td>3000.953</td>\n",
       "      <td>3049.103</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>3017.445</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>0.028850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>3087.529</td>\n",
       "      <td>3194.722</td>\n",
       "      <td>3358.588</td>\n",
       "      <td>3153.697</td>\n",
       "      <td>3336.497</td>\n",
       "      <td>0.080637</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>7223 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Preclose      Open   Highest    Lowest     Close  Raw_return\n",
       "Day                                                                     \n",
       "1995-01-03   647.870   637.720   647.710   630.530   639.880   -0.012333\n",
       "1995-01-04   639.880   641.900   655.510   638.860   653.810    0.021770\n",
       "1995-01-05   653.810   655.380   657.520   645.810   646.890   -0.010584\n",
       "1995-01-06   646.890   642.750   643.890   636.330   640.760   -0.009476\n",
       "1995-01-09   640.760   637.520   637.550   625.040   626.000   -0.023035\n",
       "...              ...       ...       ...       ...       ...         ...\n",
       "2024-09-24  2748.918  2770.754  2863.152  2761.372  2863.126    0.041547\n",
       "2024-09-25  2863.126  2901.419  2952.451  2889.048  2896.306    0.011589\n",
       "2024-09-26  2896.306  2893.745  3000.953  2889.014  3000.953    0.036131\n",
       "2024-09-27  3000.953  3049.103  3087.529  3017.445  3087.529    0.028850\n",
       "2024-09-30  3087.529  3194.722  3358.588  3153.697  3336.497    0.080637\n",
       "\n",
       "[7223 rows x 6 columns]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_new = data['1995-01':'2024-09'].copy()\n",
    "data_new['Close'] = pd.to_numeric(data_new['Close'])\n",
    "data_new['Preclose'] = pd.to_numeric(data_new['Preclose'])\n",
    "# 计算000001上证指数日收益率 两种：\n",
    "data_new['Raw_return'] = data_new['Close'] / data_new['Preclose'] - 1\n",
    "data_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
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       "      <th>1995-01-31</th>\n",
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       "      <th>1995-02-28</th>\n",
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       "      <th>1995-03-31</th>\n",
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       "      <th>1995-04-30</th>\n",
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       "      <th>1995-05-31</th>\n",
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       "      <th>...</th>\n",
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       "      <th>2024-05-31</th>\n",
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       "      <th>2024-06-30</th>\n",
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       "      <th>2024-07-31</th>\n",
       "      <td>-0.009656</td>\n",
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       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
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       "      <th>2024-09-30</th>\n",
       "      <td>0.173908</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>357 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "month                 \n",
       "1995-01-31   -0.131631\n",
       "1995-02-28   -0.023694\n",
       "1995-03-31    0.177803\n",
       "1995-04-30   -0.103552\n",
       "1995-05-31    0.207922\n",
       "...                ...\n",
       "2024-05-31   -0.005801\n",
       "2024-06-30   -0.038684\n",
       "2024-07-31   -0.009656\n",
       "2024-08-31   -0.032849\n",
       "2024-09-30    0.173908\n",
       "\n",
       "[357 rows x 1 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data = data_new.resample('ME')['Raw_return'].apply(lambda x: (1+x).prod() - 1).to_frame()\n",
    "Month_data.reset_index(inplace = True)\n",
    "Month_data.rename(columns = {'Day':'month'}, inplace = True)\n",
    "Month_data.set_index('month', inplace = True)\n",
    "Month_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.microsoft.datawrangler.viewer.v0+json": {
       "columns": [
        {
         "name": "Q",
         "rawType": "datetime64[ns]",
         "type": "datetime"
        },
        {
         "name": "Raw_return",
         "rawType": "float64",
         "type": "float"
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       "ref": "cd79f084-ba6c-4482-9bf3-aabda63797ac",
       "rows": [
        [
         "1995-03-31 00:00:00",
         "-0.0014663435565778205"
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        [
         "1995-06-30 00:00:00",
         "-0.025258146293204442"
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        [
         "1995-09-30 00:00:00",
         "0.14565955152399312"
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        [
         "1995-12-31 00:00:00",
         "-0.23135805545173949"
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        [
         "1996-03-31 00:00:00",
         "0.0019809468926146323"
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        [
         "1996-06-30 00:00:00",
         "0.4454788907061591"
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        [
         "1996-09-30 00:00:00",
         "0.08862915760024848"
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        [
         "1996-12-31 00:00:00",
         "0.047388439002661986"
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        [
         "1997-03-31 00:00:00",
         "0.3463392292425469"
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        [
         "1997-06-30 00:00:00",
         "0.012675965074272488"
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        [
         "1997-09-30 00:00:00",
         "-0.12228558631335595"
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        [
         "1997-12-31 00:00:00",
         "0.08813719951156318"
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        [
         "1998-03-31 00:00:00",
         "0.040968093124528426"
        ],
        [
         "1998-06-30 00:00:00",
         "0.07737606796350804"
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        [
         "1998-09-30 00:00:00",
         "-0.07190860215053663"
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        [
         "1998-12-31 00:00:00",
         "-0.07739962989781946"
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        [
         "1999-03-31 00:00:00",
         "0.009897968082323017"
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        [
         "1999-06-30 00:00:00",
         "0.4588575622814226"
        ],
        [
         "1999-09-30 00:00:00",
         "-0.07027814114819786"
        ],
        [
         "1999-12-31 00:00:00",
         "-0.12995479722416803"
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        [
         "2000-03-31 00:00:00",
         "0.31731768356042234"
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        [
         "2000-06-30 00:00:00",
         "0.07104131717234563"
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        [
         "2000-09-30 00:00:00",
         "-0.009309634823738921"
        ],
        [
         "2000-12-31 00:00:00",
         "0.08550069104158786"
        ],
        [
         "2001-03-31 00:00:00",
         "0.018953643150645627"
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        [
         "2001-06-30 00:00:00",
         "0.04981588239192014"
        ],
        [
         "2001-09-30 00:00:00",
         "-0.20430742595907236"
        ],
        [
         "2001-12-31 00:00:00",
         "-0.06737040121935234"
        ],
        [
         "2002-03-31 00:00:00",
         "-0.02555939658681483"
        ],
        [
         "2002-06-30 00:00:00",
         "0.08034166718623315"
        ],
        [
         "2002-09-30 00:00:00",
         "-0.08722500519402487"
        ],
        [
         "2002-12-31 00:00:00",
         "-0.14160797157344995"
        ],
        [
         "2003-03-31 00:00:00",
         "0.11264317018377268"
        ],
        [
         "2003-06-30 00:00:00",
         "-0.016258655615723483"
        ],
        [
         "2003-09-30 00:00:00",
         "-0.07998546452941402"
        ],
        [
         "2003-12-31 00:00:00",
         "0.09499985371134367"
        ],
        [
         "2004-03-31 00:00:00",
         "0.1633757281034569"
        ],
        [
         "2004-06-30 00:00:00",
         "-0.19663301983211112"
        ],
        [
         "2004-09-30 00:00:00",
         "-0.0017581977758082123"
        ],
        [
         "2004-12-31 00:00:00",
         "-0.09321973222596158"
        ],
        [
         "2005-03-31 00:00:00",
         "-0.06731938412949057"
        ],
        [
         "2005-06-30 00:00:00",
         "-0.08491077173140127"
        ],
        [
         "2005-09-30 00:00:00",
         "0.06907876477880315"
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        [
         "2005-12-31 00:00:00",
         "0.00471612395185228"
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        [
         "2006-03-31 00:00:00",
         "0.11820233235147315"
        ],
        [
         "2006-06-30 00:00:00",
         "0.28799969190479713"
        ],
        [
         "2006-09-30 00:00:00",
         "0.04796646354225853"
        ],
        [
         "2006-12-31 00:00:00",
         "0.5267287522397601"
        ],
        [
         "2007-03-31 00:00:00",
         "0.1900638018740637"
        ],
        [
         "2007-06-30 00:00:00",
         "0.19997613050333118"
        ]
       ],
       "shape": {
        "columns": 1,
        "rows": 119
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Q</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>-0.001466</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-06-30</th>\n",
       "      <td>-0.025258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-09-30</th>\n",
       "      <td>0.145660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-12-31</th>\n",
       "      <td>-0.231358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996-03-31</th>\n",
       "      <td>0.001981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-30</th>\n",
       "      <td>-0.028603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>-0.043575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-03-31</th>\n",
       "      <td>0.022263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.024255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.124383</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>119 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Q                     \n",
       "1995-03-31   -0.001466\n",
       "1995-06-30   -0.025258\n",
       "1995-09-30    0.145660\n",
       "1995-12-31   -0.231358\n",
       "1996-03-31    0.001981\n",
       "...                ...\n",
       "2023-09-30   -0.028603\n",
       "2023-12-31   -0.043575\n",
       "2024-03-31    0.022263\n",
       "2024-06-30   -0.024255\n",
       "2024-09-30    0.124383\n",
       "\n",
       "[119 rows x 1 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Quarter_data = data_new.resample('QE')['Raw_return'].apply(lambda x: (1+x).prod() - 1).to_frame()\n",
    "Quarter_data.reset_index(inplace = True)\n",
    "Quarter_data.rename(columns = {'Day':'Q'}, inplace = True)\n",
    "Quarter_data.set_index('Q', inplace = True)\n",
    "Quarter_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.microsoft.datawrangler.viewer.v0+json": {
       "columns": [
        {
         "name": "Year",
         "rawType": "datetime64[ns]",
         "type": "datetime"
        },
        {
         "name": "Raw_return",
         "rawType": "float64",
         "type": "float"
        }
       ],
       "ref": "ac8576ae-2b4b-49b9-9f96-034e2e1381fa",
       "rows": [
        [
         "1995-12-31 00:00:00",
         "-0.1428990383873303"
        ],
        [
         "1996-12-31 00:00:00",
         "0.6514253813322783"
        ],
        [
         "1997-12-31 00:00:00",
         "0.3021526248064368"
        ],
        [
         "1998-12-31 00:00:00",
         "-0.03969516790888461"
        ],
        [
         "1999-12-31 00:00:00",
         "0.19175023981861106"
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        [
         "2000-12-31 00:00:00",
         "0.5172767053520502"
        ],
        [
         "2001-12-31 00:00:00",
         "-0.2061799486853021"
        ],
        [
         "2002-12-31 00:00:00",
         "-0.1751672266201686"
        ],
        [
         "2003-12-31 00:00:00",
         "0.10267005487423031"
        ],
        [
         "2004-12-31 00:00:00",
         "-0.1539972211831364"
        ],
        [
         "2005-12-31 00:00:00",
         "-0.08325305961310714"
        ],
        [
         "2006-12-31 00:00:00",
         "1.3043339706819643"
        ],
        [
         "2007-12-31 00:00:00",
         "0.9665927855666503"
        ],
        [
         "2008-12-31 00:00:00",
         "-0.6539410364986822"
        ],
        [
         "2009-12-31 00:00:00",
         "0.7998253524530277"
        ],
        [
         "2010-12-31 00:00:00",
         "-0.14313090072441115"
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        [
         "2011-12-31 00:00:00",
         "-0.21675308395772197"
        ],
        [
         "2012-12-31 00:00:00",
         "0.03169471951696434"
        ],
        [
         "2013-12-31 00:00:00",
         "-0.06749282764760167"
        ],
        [
         "2014-12-31 00:00:00",
         "0.5286911974593327"
        ],
        [
         "2015-12-31 00:00:00",
         "0.09413605055214114"
        ],
        [
         "2016-12-31 00:00:00",
         "-0.12306240428573822"
        ],
        [
         "2017-12-31 00:00:00",
         "0.06557783763580938"
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        [
         "2018-12-31 00:00:00",
         "-0.24591115666869323"
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        [
         "2019-12-31 00:00:00",
         "0.22303219856449563"
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        [
         "2020-12-31 00:00:00",
         "0.1386666754094923"
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        [
         "2021-12-31 00:00:00",
         "0.04800076013440857"
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        [
         "2022-12-31 00:00:00",
         "-0.1512503907782794"
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        [
         "2023-12-31 00:00:00",
         "-0.03700665457551999"
        ],
        [
         "2024-12-31 00:00:00",
         "0.12153617618779378"
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Year</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-12-31</th>\n",
       "      <td>-0.142899</td>\n",
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       "    <tr>\n",
       "      <th>1996-12-31</th>\n",
       "      <td>0.651425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-12-31</th>\n",
       "      <td>0.302153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998-12-31</th>\n",
       "      <td>-0.039695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1999-12-31</th>\n",
       "      <td>0.191750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-12-31</th>\n",
       "      <td>0.517277</td>\n",
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       "    <tr>\n",
       "      <th>2001-12-31</th>\n",
       "      <td>-0.206180</td>\n",
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       "    <tr>\n",
       "      <th>2002-12-31</th>\n",
       "      <td>-0.175167</td>\n",
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       "    <tr>\n",
       "      <th>2003-12-31</th>\n",
       "      <td>0.102670</td>\n",
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       "      <th>2004-12-31</th>\n",
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       "      <th>2005-12-31</th>\n",
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       "    <tr>\n",
       "      <th>2006-12-31</th>\n",
       "      <td>1.304334</td>\n",
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       "    <tr>\n",
       "      <th>2007-12-31</th>\n",
       "      <td>0.966593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-12-31</th>\n",
       "      <td>-0.653941</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-12-31</th>\n",
       "      <td>0.799825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-12-31</th>\n",
       "      <td>-0.143131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-12-31</th>\n",
       "      <td>-0.216753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-12-31</th>\n",
       "      <td>0.031695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-31</th>\n",
       "      <td>-0.067493</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-31</th>\n",
       "      <td>0.528691</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-31</th>\n",
       "      <td>0.094136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-31</th>\n",
       "      <td>-0.123062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-31</th>\n",
       "      <td>0.065578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-12-31</th>\n",
       "      <td>-0.245911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-12-31</th>\n",
       "      <td>0.223032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-12-31</th>\n",
       "      <td>0.138667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-12-31</th>\n",
       "      <td>0.048001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-12-31</th>\n",
       "      <td>-0.151250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>-0.037007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>0.121536</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Year                  \n",
       "1995-12-31   -0.142899\n",
       "1996-12-31    0.651425\n",
       "1997-12-31    0.302153\n",
       "1998-12-31   -0.039695\n",
       "1999-12-31    0.191750\n",
       "2000-12-31    0.517277\n",
       "2001-12-31   -0.206180\n",
       "2002-12-31   -0.175167\n",
       "2003-12-31    0.102670\n",
       "2004-12-31   -0.153997\n",
       "2005-12-31   -0.083253\n",
       "2006-12-31    1.304334\n",
       "2007-12-31    0.966593\n",
       "2008-12-31   -0.653941\n",
       "2009-12-31    0.799825\n",
       "2010-12-31   -0.143131\n",
       "2011-12-31   -0.216753\n",
       "2012-12-31    0.031695\n",
       "2013-12-31   -0.067493\n",
       "2014-12-31    0.528691\n",
       "2015-12-31    0.094136\n",
       "2016-12-31   -0.123062\n",
       "2017-12-31    0.065578\n",
       "2018-12-31   -0.245911\n",
       "2019-12-31    0.223032\n",
       "2020-12-31    0.138667\n",
       "2021-12-31    0.048001\n",
       "2022-12-31   -0.151250\n",
       "2023-12-31   -0.037007\n",
       "2024-12-31    0.121536"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Year_data = data_new.resample('YE')['Raw_return'].apply(lambda x: (1+x).prod() - 1).to_frame()\n",
    "Year_data.reset_index(inplace = True)\n",
    "Year_data.rename(columns = {'Day':'Year'}, inplace = True)\n",
    "Year_data.set_index('Year', inplace = True)\n",
    "Year_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.microsoft.datawrangler.viewer.v0+json": {
       "columns": [
        {
         "name": "month",
         "rawType": "datetime64[ns]",
         "type": "datetime"
        },
        {
         "name": "cpi",
         "rawType": "float64",
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       "            cpi\n",
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       "1987-01-31  5.1\n",
       "1987-02-28  5.4\n",
       "1987-03-31  5.8\n",
       "1987-04-30  6.7\n",
       "1987-05-31  7.6\n",
       "...         ...\n",
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       "\n",
       "[453 rows x 1 columns]"
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     "execution_count": 16,
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   "source": [
    "inflation = pd.read_csv('datasets/inflation.csv')\n",
    "inflation['month'] = pd.to_datetime(inflation['month'],format='%Y/%m/%d')\n",
    "inflation.set_index('month',inplace=True)\n",
    "inflation.sort_values(by=['month'],axis=0,ascending=True)"
   ]
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  {
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       "                  RV\n",
       "month               \n",
       "1995-01-31  0.005695\n",
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       "1995-03-31  0.013378\n",
       "1995-04-30  0.008281\n",
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     "execution_count": 17,
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   "source": [
    "# ICAPM 模型的简化版\n",
    "market_variance = data_new.resample('ME').apply({\n",
    "    'Raw_return':\n",
    "    lambda x: sum(x**2)\n",
    "})\n",
    "market_variance.reset_index(inplace=True)\n",
    "market_variance.rename(columns={'Day':'month','Raw_return':'RV'},inplace=True)\n",
    "market_variance.set_index('month',inplace=True)\n",
    "market_variance\n",
    "\n",
    "# market_variance <- daily_data[,.(MV = sum(Raw_return^2)),by = 'month'] This is R code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
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       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 2000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#作图\n",
    "reg_data_plot = reg_data['2000-01':'2024-09'].copy()\n",
    "# Plot the China's stock market return and inflation into one graph\n",
    "fig, ax1 = plt.subplots(figsize=(20,5))\n",
    "# the linewidth and marker size are set to be very small\n",
    "ax1.plot(reg_data_plot['Raw_return'],color='red',marker='o',linewidth=0.8,\n",
    "         markersize=4,\n",
    "         linestyle='-',label='China Stock Market Return')\n",
    "ax1.set_ylabel('China Stock Market Return',color='red')\n",
    "#ax1.set_xlabel('Month')\n",
    "\n",
    "# 设置x轴的日期显示格式\n",
    "data_format = mdates.DateFormatter('%Y')\n",
    "ax1.xaxis.set_major_formatter(data_format)\n",
    "ax1.xaxis.set_major_locator(mdates.YearLocator())\n",
    "\n",
    "# 转置x轴的日期显示格式\n",
    "plt.xticks(rotation = 90)\n",
    "\n",
    "\n",
    "ax2 = ax1.twinx()\n",
    "ax2.plot(reg_data_plot['RV'].shift(1),color='blue',marker='o',linewidth=0.8,\n",
    "         markersize=4,\n",
    "         linestyle='-',label='Realized Variance')\n",
    "\n",
    "ax2.set_ylabel('Realized Variance',color='blue')\n",
    "\n",
    "plt.title('China Stock Market Return and Realized Variance')\n",
    "\n",
    "# change the legend into one box\n",
    "lines, labels = ax1.get_legend_handles_labels()\n",
    "lines2, labels2 = ax2.get_legend_handles_labels()\n",
    "ax2.legend(lines + lines2, labels + labels2, loc='upper right')\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.microsoft.datawrangler.viewer.v0+json": {
       "columns": [
        {
         "name": "index",
         "rawType": "object",
         "type": "string"
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         "name": "RV",
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       ],
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         "count",
         "357.0"
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         "std",
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         "min",
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         "25%",
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         "50%",
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         "75%",
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         "max",
         "0.14839"
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       "count    357.00000\n",
       "mean       0.00549\n",
       "std        0.00971\n",
       "min        0.00016\n",
       "25%        0.00155\n",
       "50%        0.00277\n",
       "75%        0.00605\n",
       "max        0.14839\n",
       "Name: RV, dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 描述性统计\n",
    "reg_data['RV'].describe().round(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(9.699442671747752)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
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    {
     "data": {
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       "np.float64(133.47698299206684)"
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     "execution_count": 20,
     "metadata": {},
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    }
   ],
   "source": [
    "reg_data['RV'].skew()\n",
    "reg_data['RV'].kurt()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             Raw_return   R-squared:                       0.003\n",
      "Model:                            OLS   Adj. R-squared:                  0.000\n",
      "Method:                 Least Squares   F-statistic:                     1.417\n",
      "Date:                 周一, 17 11月 2025   Prob (F-statistic):              0.235\n",
      "Time:                        10:02:12   Log-Likelihood:                 414.52\n",
      "No. Observations:                 356   AIC:                            -825.0\n",
      "Df Residuals:                     354   BIC:                            -817.3\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0103      0.005      2.171      0.030       0.001       0.020\n",
      "lRV           -0.4414      0.371     -1.190      0.234      -1.168       0.285\n",
      "==============================================================================\n",
      "Omnibus:                       27.368   Durbin-Watson:                   1.850\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               63.074\n",
      "Skew:                           0.379   Prob(JB):                     2.01e-14\n",
      "Kurtosis:                       4.918   Cond. No.                         103.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "# OLS 回归结果\n",
    "reg_data['lRV'] = reg_data['RV'].shift(1)\n",
    "model_cpi = smf.ols('Raw_return ~ lRV',\n",
    "                 data=reg_data['1995-01':'2024-09']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model_cpi.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             Raw_return   R-squared:                       0.040\n",
      "Model:                            OLS   Adj. R-squared:                  0.037\n",
      "Method:                 Least Squares   F-statistic:                     9.517\n",
      "Date:                 周一, 17 11月 2025   Prob (F-statistic):            0.00223\n",
      "Time:                        10:02:12   Log-Likelihood:                 371.45\n",
      "No. Observations:                 297   AIC:                            -738.9\n",
      "Df Residuals:                     295   BIC:                            -731.5\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0204      0.007      3.021      0.003       0.007       0.034\n",
      "lcpi          -0.0073      0.002     -3.085      0.002      -0.012      -0.003\n",
      "==============================================================================\n",
      "Omnibus:                       14.674   Durbin-Watson:                   1.808\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               36.741\n",
      "Skew:                           0.050   Prob(JB):                     1.05e-08\n",
      "Kurtosis:                       4.720   Cond. No.                         4.35\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "reg_data['lcpi'] = reg_data['cpi'].shift(2)\n",
    "model_cpi = smf.ols('Raw_return ~ lcpi',\n",
    "                 data=reg_data['2000-01':'2024-09']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model_cpi.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             Raw_return   R-squared:                       0.043\n",
      "Model:                            OLS   Adj. R-squared:                  0.036\n",
      "Method:                 Least Squares   F-statistic:                     5.340\n",
      "Date:                 周一, 17 11月 2025   Prob (F-statistic):            0.00527\n",
      "Time:                        10:02:12   Log-Likelihood:                 371.82\n",
      "No. Observations:                 297   AIC:                            -737.6\n",
      "Df Residuals:                     294   BIC:                            -726.6\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0226      0.007      3.032      0.002       0.008       0.037\n",
      "lRV           -0.6994      1.158     -0.604      0.546      -2.970       1.571\n",
      "lcpi          -0.0069      0.002     -3.124      0.002      -0.011      -0.003\n",
      "==============================================================================\n",
      "Omnibus:                       14.182   Durbin-Watson:                   1.818\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               33.162\n",
      "Skew:                           0.106   Prob(JB):                     6.30e-08\n",
      "Kurtosis:                       4.623   Cond. No.                         583.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "model_twovariables = smf.ols('Raw_return ~ lRV + lcpi',\n",
    "                 data=reg_data['2000-01':'2024-09']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model_twovariables.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "      <th>RV</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>-0.001466</td>\n",
       "      <td>0.037159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-06-30</th>\n",
       "      <td>-0.025258</td>\n",
       "      <td>0.165852</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-09-30</th>\n",
       "      <td>0.145660</td>\n",
       "      <td>0.022866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-12-31</th>\n",
       "      <td>-0.231358</td>\n",
       "      <td>0.014829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996-03-31</th>\n",
       "      <td>0.001981</td>\n",
       "      <td>0.021250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-30</th>\n",
       "      <td>-0.028603</td>\n",
       "      <td>0.003941</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>-0.043575</td>\n",
       "      <td>0.002575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-03-31</th>\n",
       "      <td>0.022263</td>\n",
       "      <td>0.007629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.024255</td>\n",
       "      <td>0.003100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.124383</td>\n",
       "      <td>0.013191</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>119 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return        RV\n",
       "month                           \n",
       "1995-03-31   -0.001466  0.037159\n",
       "1995-06-30   -0.025258  0.165852\n",
       "1995-09-30    0.145660  0.022866\n",
       "1995-12-31   -0.231358  0.014829\n",
       "1996-03-31    0.001981  0.021250\n",
       "...                ...       ...\n",
       "2023-09-30   -0.028603  0.003941\n",
       "2023-12-31   -0.043575  0.002575\n",
       "2024-03-31    0.022263  0.007629\n",
       "2024-06-30   -0.024255  0.003100\n",
       "2024-09-30    0.124383  0.013191\n",
       "\n",
       "[119 rows x 2 columns]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 季度结果\n",
    "Q_reg_data = reg_data['1995-01':'2024-09'].resample('QE').apply({\n",
    "    'Raw_return':\n",
    "    lambda x: np.prod(1+x) - 1,\n",
    "    'RV':\n",
    "    lambda x: sum(x)\n",
    "})\n",
    "Q_reg_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
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       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- 2001 -->\n",
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       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
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       "    </g>\n",
       "    <g id=\"xtick_10\">\n",
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       "     <g id=\"text_10\">\n",
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       "    </g>\n",
       "    <g id=\"xtick_12\">\n",
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       "    </g>\n",
       "    <g id=\"xtick_13\">\n",
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       "       <use xlink:href=\"#DejaVuSans-30\" transform=\"translate(127.246094 0)\"/>\n",
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       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_14\">\n",
       "     <g id=\"line2d_14\">\n",
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       "     <g id=\"text_14\">\n",
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       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_15\">\n",
       "     <g id=\"line2d_15\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mfb52191bc6\" x=\"296.843768\" y=\"299.518125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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       "     </g>\n",
       "     <g id=\"text_15\">\n",
       "      <!-- 2008 -->\n",
       "      <g transform=\"translate(299.603143 331.968125) rotate(-90) scale(0.1 -0.1)\">\n",
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       "       <use xlink:href=\"#DejaVuSans-30\" transform=\"translate(127.246094 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-38\" transform=\"translate(190.869141 0)\"/>\n",
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       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_16\">\n",
       "     <g id=\"line2d_16\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mfb52191bc6\" x=\"314.072964\" y=\"299.518125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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       "     <g id=\"text_16\">\n",
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       "    </g>\n",
       "    <g id=\"xtick_17\">\n",
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       "    </g>\n",
       "    <g id=\"xtick_18\">\n",
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       "    </g>\n",
       "    <g id=\"xtick_20\">\n",
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       "       <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(127.246094 0)\"/>\n",
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       "    </g>\n",
       "    <g id=\"xtick_21\">\n",
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       "    </g>\n",
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       "    <g id=\"xtick_23\">\n",
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       "    <g id=\"xtick_25\">\n",
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       "    <g id=\"xtick_27\">\n",
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       "    <g id=\"xtick_28\">\n",
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      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the China's stock market return and inflation into one graph\n",
    "fig, ax1 = plt.subplots(figsize=(10,5))\n",
    "# the linewidth and marker size are set to be very small\n",
    "ax1.plot(Q_reg_data['Raw_return'],color='red',marker='o',linewidth=0.8,\n",
    "         markersize=4,\n",
    "         linestyle='-',label='China Stock Market Return')\n",
    "ax1.set_ylabel('China Stock Market Return',color='red')\n",
    "#ax1.set_xlabel('Month')\n",
    "\n",
    "# 设置x轴的日期显示格式\n",
    "data_format = mdates.DateFormatter('%Y')\n",
    "ax1.xaxis.set_major_formatter(data_format)\n",
    "ax1.xaxis.set_major_locator(mdates.YearLocator())\n",
    "\n",
    "# 转置x轴的日期显示格式\n",
    "plt.xticks(rotation = 90)\n",
    "\n",
    "ax2 = ax1.twinx()\n",
    "ax2.plot(Q_reg_data['RV'].shift(1),color='blue',marker='o',linewidth=0.8,\n",
    "         markersize=4,\n",
    "         linestyle='-',label='Realized Variance')\n",
    "\n",
    "ax2.set_ylabel('Realized Variance',color='blue')\n",
    "\n",
    "plt.title('China Stock Market Return and Realized Variance')\n",
    "\n",
    "# change the legend into one box\n",
    "lines, labels = ax1.get_legend_handles_labels()\n",
    "lines2, labels2 = ax2.get_legend_handles_labels()\n",
    "ax2.legend(lines + lines2, labels + labels2, loc='upper right')\n",
    "\n",
    "# save figure\n",
    "fig.savefig('images/China Stock Market Return and Realized Variance Quarter.png',dpi = 1000,bbox_inches='tight')\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             Raw_return   R-squared:                       0.000\n",
      "Model:                            OLS   Adj. R-squared:                 -0.010\n",
      "Method:                 Least Squares   F-statistic:                   0.02161\n",
      "Date:                Tue, 29 Oct 2024   Prob (F-statistic):              0.883\n",
      "Time:                        10:05:11   Log-Likelihood:                 52.471\n",
      "No. Observations:                  99   AIC:                            -100.9\n",
      "Df Residuals:                      97   BIC:                            -95.75\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0166      0.020      0.832      0.406      -0.022       0.056\n",
      "lRV            0.1625      1.105      0.147      0.883      -2.004       2.329\n",
      "==============================================================================\n",
      "Omnibus:                       14.494   Durbin-Watson:                   1.584\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               20.110\n",
      "Skew:                           0.697   Prob(JB):                     4.30e-05\n",
      "Kurtosis:                       4.713   Cond. No.                         77.4\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "Q_reg_data['lRV'] = Q_reg_data['RV'].shift(1)\n",
    "model_qcpi = smf.ols('Raw_return ~ lRV',\n",
    "                 data=Q_reg_data['2000-01':'2024-09']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model_qcpi.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
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       "      <th>Raw_return</th>\n",
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       "      <th>1995-01-31</th>\n",
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       "      <td>0.001542</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>357 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return        RV   cpi       lRV  lcpi  next_ret  next_ret2  \\\n",
       "month                                                                         \n",
       "1995-01-31   -0.131631  0.005695  24.1       NaN   NaN  0.976306   1.177803   \n",
       "1995-02-28   -0.023694  0.018086  22.4  0.005695   NaN  1.177803   0.896448   \n",
       "1995-03-31    0.177803  0.013378  21.3  0.018086  24.1  0.896448   1.207922   \n",
       "1995-04-30   -0.103552  0.008281  20.7  0.013378  22.4  1.207922   0.900173   \n",
       "1995-05-31    0.207922  0.148387  20.3  0.008281  21.3  0.900173   1.103032   \n",
       "...                ...       ...   ...       ...   ...       ...        ...   \n",
       "2024-05-31   -0.005801  0.000915   0.3  0.001542   0.1  0.961316   0.990344   \n",
       "2024-06-30   -0.038684  0.000642   0.2  0.000915   0.3  0.990344   0.967151   \n",
       "2024-07-31   -0.009656  0.001441   0.5  0.000642   0.3  0.967151   1.173908   \n",
       "2024-08-31   -0.032849  0.000705   0.6  0.001441   0.2  1.173908        NaN   \n",
       "2024-09-30    0.173908  0.011045   0.4  0.000705   0.5       NaN        NaN   \n",
       "\n",
       "            next_ret3  future_3month_return  \n",
       "month                                        \n",
       "1995-01-31   0.896448              0.030822  \n",
       "1995-02-28   1.207922              0.275370  \n",
       "1995-03-31   0.900173             -0.025258  \n",
       "1995-04-30   1.103032              0.199369  \n",
       "1995-05-31   1.040716              0.033347  \n",
       "...               ...                   ...  \n",
       "2024-05-31   0.967151             -0.079240  \n",
       "2024-06-30   1.173908              0.124383  \n",
       "2024-07-31        NaN                   NaN  \n",
       "2024-08-31        NaN                   NaN  \n",
       "2024-09-30        NaN                   NaN  \n",
       "\n",
       "[357 rows x 9 columns]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 长期预测\n",
    "reg_data['next_ret'] = reg_data['Raw_return'].shift(-1) + 1\n",
    "reg_data['next_ret2'] = reg_data['Raw_return'].shift(-2) + 1\n",
    "reg_data['next_ret3'] = reg_data['Raw_return'].shift(-3) + 1\n",
    "reg_data['future_3month_return'] = reg_data['next_ret'] * reg_data['next_ret2'] * reg_data['next_ret3'] - 1\n",
    "reg_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                             OLS Regression Results                             \n",
      "================================================================================\n",
      "Dep. Variable:     future_3month_return   R-squared:                       0.000\n",
      "Model:                              OLS   Adj. R-squared:                 -0.003\n",
      "Method:                   Least Squares   F-statistic:                  0.008066\n",
      "Date:                  Tue, 29 Oct 2024   Prob (F-statistic):              0.928\n",
      "Time:                          10:05:11   Log-Likelihood:                 164.02\n",
      "No. Observations:                   294   AIC:                            -324.0\n",
      "Df Residuals:                       292   BIC:                            -316.7\n",
      "Df Model:                             1                                         \n",
      "Covariance Type:                    HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0165      0.015      1.097      0.273      -0.013       0.046\n",
      "RV            -0.3083      3.433     -0.090      0.928      -7.036       6.419\n",
      "==============================================================================\n",
      "Omnibus:                       36.547   Durbin-Watson:                   0.522\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               59.280\n",
      "Skew:                           0.741   Prob(JB):                     1.34e-13\n",
      "Kurtosis:                       4.625   Cond. No.                         195.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "model_cpi_3month = smf.ols('future_3month_return ~ RV',\n",
    "                 data=reg_data['2000-01':'2024-09']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model_cpi_3month.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                     RV   R-squared:                       0.377\n",
      "Model:                            OLS   Adj. R-squared:                  0.373\n",
      "Method:                 Least Squares   F-statistic:                     30.98\n",
      "Date:                Tue, 29 Oct 2024   Prob (F-statistic):           6.16e-13\n",
      "Time:                        10:05:11   Log-Likelihood:                 1214.9\n",
      "No. Observations:                 297   AIC:                            -2424.\n",
      "Df Residuals:                     294   BIC:                            -2413.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0013      0.000      3.118      0.002       0.000       0.002\n",
      "lRV            0.5841      0.084      6.949      0.000       0.419       0.749\n",
      "lcpi           0.0003      0.000      1.308      0.191      -0.000       0.001\n",
      "==============================================================================\n",
      "Omnibus:                      124.542   Durbin-Watson:                   2.191\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              493.512\n",
      "Skew:                           1.786   Prob(JB):                    6.84e-108\n",
      "Kurtosis:                       8.207   Cond. No.                         583.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "# 预测波动率\n",
    "model_mv = smf.ols('RV ~ lRV + lcpi',\n",
    "                 data=reg_data['2000-01':'2024-09']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model_mv.summary())"
   ]
  }
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